MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation 1

Sparse Reconstruction and Feature Extraction

MURI Review Meeting

Lee Potter, Müjdat Çetin, Emre Ertin, Clem Karl, Randy Moses

September 14, 2007

Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation

MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation 2

Draft inputs: OSU signal processing

Recursive imaging Wide-angle sparse imaging Bayesian sparse linear regression

(FBMP)

MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation 3

Recursive Image Updating for Persistent Synthetic Aperture Radar Surveillance

Persistent SAR SAR video Imagery on demand Variable aperture integration

Insight: recursive imaging spreads computation over time and avoids block processing memory load

MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation 4

Convolution Backprojection

Range profile by filtering and backprojecting

Window wj controls crossrange sidelobes J N2 computations per image Recursive formulation:

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MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation 5

Third Order Recursion

Can choose i coefficients to emulate many common apodization windows (e.g. Hamming).

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Azimuth sample

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MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation 6

GOTCHA C-SAR Video Snapshots

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GOTCHA: fc=9.6 GHz, 640 MHz BW, 45 elev, 3 azimuth

Block-Processing

Hamming Az Window

Recursive Processing

Third Order

MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation 7

Flop-free change in effective aperture

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Recursive Processing

3° Azimuth Window

Recursive Processing

25° Azimuth Window

MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation 8

Wide-Angle Sparse 3D Synthetic Aperture Radar

“Squiggle” Path Dataset

Air Force Research Laboratory construction backhoe challenge dataset

Data collected over a very sparse “squiggle” flight path

Radar: fc: 10 GHz, BW 6 GHz

Polarization: HH, VV, VH

Az [65.5, 114.5]El [17.5, 42.5]

k-space

Squiggle PSF

MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation 9

Approach

Insights Sparsity of strong reflectors Low persistence: uncorrelated

subimages Approach

Form narrow-angle sub-images by l1-penalized least-squares inversion

Noncoherently combine subaperture images

k-space

MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation 10

Results

1.29% data of benchmark

MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation 11

Animation

MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation 12

Sparse Linear Regression: FBMP

“Are you guys still working on As + n ?”

Thomas Kailath, c. 1988

“The thing that hath been, it is that which shall be; and that which is done is that which shall be done: and there is no new thing under the sun.”

Ecclesiastes 1:9, c. BC 250

“There is nothing new under the sun but there are lots of old things we don't know.”

Ambrose Bierce, The Devil's Dictionary, US author & satirist (1842 - 1914)

“Neurosis is the inability to tolerate ambiguity.”

Sigmund Freud (1856 – 1939)

[graphic courtesy of Rich Baraniuk]

MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation 13

Desiderata

Allow arbitrary correlation of columns in design matrix Ambiguity in variable selection

Report ambiguity Compute posterior probabilities for variable sets & posterior on

vbls Minimize estimation error

MMSE estimation of variables Compute with low complexity

Keep order of complexity of Orthogonal Matched Pursuits Use domain knowledge, if available

Flexible family of priors with known hyperparameters, or ML estimation of hyperparameters

Admit complex-valued data Band-pass signals in radar, spectroscopy and communications

Provide non-asymptotic bounds on variable detection Characterize performance of the MAP detection of variables

MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation 14

Applications: Radar

Radar: Wide Area-Coverage, all weather, day/night, persistent illumination

High resolution imaging of objects and tracking of moving targets

MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation 15

In a Nutshell…

Bayesian signal model Effective tree search for high-probability set Fast update of posterior Generalized EM for unknown hyperparameters

Return MAP solution, MMSE solution and list of candidate solutions with relative probabilities

MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation 16

Signal Model Variables drawn from a Gaussian mixture with

point mass at origin Multinomial for mixing indicator Simplest illustration:

Procedures implemented for complex-valued case and arbitrary Gaussian mixtures

0

MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation 17

Model Posteriors

MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation 18

Posterior, p(x|y)

Typical realization: s_true ranks fourth in p(s | y)

MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation 19

NMSE

9 dB

MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation 20

Sparsity

MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation 21

Runtime

“Fast” but no free lunch

MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation 22

MAP detection bounds

Perfect detection is very low probability

1. Sufficient condition for detection of a coefficient with probability 1-δ

2. Necessary condition for detection of a coefficient with probability 1-δ

3. Sufficient condition for detection of 1-ε energy with probability 1-δ